Is drinking multiple glasses of black tea and/or green tea each day healthy, or would that be an excessive exposure despite reported health benefits of “regular” tea drinking?

This is completely safe for you and for almost all people. There are some, as you know, who cannot tolerate caffeine and that is a separate matter. It is not that it is dangerous, it is that it is upsetting to their nervous system and they will simply not like the feelings it generates. That is true of tea in general, that when one reaches a level that is excessive for their body, they will feel something amiss and will make a mental association that perhaps they had too much tea and then may moderate a bit. So there is a built-in safety mechanism that will prevent such things from getting out of hand. There is nothing of danger that can produce a long-term chronic health liability, it is only when acute intake rises above a certain threshold and one feels inner disquiet that you will know the body is unhappy and can make note to back off a bit and that is all that is needed here. There is no great danger in what happens, it is very much akin to the caffeine‑sensitive person who will feel innervated and may have trouble sleeping because they feel wired, so to speak. That is not a great danger, only an inconvenience.